Problem: The equation of a circle $C$ is $x^2+y^2+10y+9 = 0$. What is its center $(h, k)$ and its radius $r$ ?
Solution: To find the equation in standard form, complete the square. $(x^2) + (y^2+10y) = -9$ $(x^2) + (y^2+10y+25) = -9 + 0 + 25$ $x^2 + (y+5)^{2} = 16 = 4^2$ Thus, $(h, k) = (0, -5)$ and $r = 4$.